As has been mentioned in the Introduction, in Refs. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, various criteria have been proposed for selecting a renormalization scheme so that a perturbative result best approximates the exact (scheme-independent) result. In this Appendix, rather than discussing any specific choice of renormalization scheme in QCD used to compute \(R(s)\)  (the cross section for \(e^+ e^-\rightarrow \)  hadrons) we show how the RG equation allows one to sum all higher order contributions to \(R(s)\)  that explicitly involve parameters that characterize the renormalization scheme being used, and that this summation leads to cancellation between this explicit dependence on these parameters and implicit dependence on these parameters through the QCD coupling \(\alpha \) . \(R(s)\)  is finally expressed as a power series in the
't Hooft coupling evaluated at \(s/\Lambda ^2\)  with coefficients that are independent of the renormaliztion scheme being used.
